Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
164 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 164 conjugacy classes of subgroups — too many to draw. Only its 70 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C7×Dic12 | C2 | semidirect |
| 3. C3×C7×M32 | C2 | semidirect |
| 4. C7×Dic24 | C2 | semidirect |
| 5. C7×#800 | C2 | semidirect |
| 20. C7×M32 | D3 | semidirect |
| 21. #4909 | C7 | direct (N × H) |
| 41. C2×Dic12 | C2×C7 | semidirect |
| 43. C3×M32 | C2×C7 | semidirect |
| 44. Dic24 | C2×C7 | semidirect |
| 45. #800 | C2×C7 | semidirect |
| 79. M32 | D3×C7 | semidirect |
| 96. C3×C7 | #510 | semidirect |
| 125. C7 | #4909 | direct (N × H) |
| 135. C3 | C7×#510 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×Dic12 | 2 |
| C7×#904 | 2 |
| C3×C7×M32 | 2 |
| C7×Dic24 | 2 |
| C7×#800 | 2 |
| C7×#510 | 3 |
| #4909 | 7 |